Method for producing group iii nitride wafers and group iii nitride wafers

ABSTRACT

The present invention discloses a method of removing contaminant from group III nitride single-crystal wafers. The method involves annealing a wafer to concentrate a contaminant in a region of the crystal near the surface of the crystal and removing some of the crystal near the surface that contains at least a portion of the region containing concentrated contaminant. The resultant thinner wafer therefore has less contaminant in it.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a continuation application of U.S. application Ser. No. 12/392,960, filed Feb. 25, 2009, and entitled “Method for Producing Group III Nitride Wafers and Group III Nitride Wafers,” inventors Tadao Hashimoto, Edward Letts, and Masanori Ikari, which claims the benefit of priority to U.S. Application Ser. No. 61/067,117, filed Feb. 25, 2008, and entitled “Method for Producing Group III Nitride Wafers and Group III Nitride Wafers,” inventors Tadao Hashimoto, Edward Letts, and Masanori Ikari, the entire contents of each of which are incorporated by reference herein as if put forth in full below. This application also incorporates by reference the International Application WO2009/108700 filed Feb. 25, 2009, entitled “Method for Producing Group III Nitride Wafers and Group III Nitride Wafers,” inventors Tadao Hashimoto, Edward Letts, and Masanori Ikari.

BACKGROUND

1. Field of the Invention

The invention is related to the production of group III nitride wafers using the ammonothermal method.

2. Further Information on Group III-Nitride Materials and Manner of Making

Gallium nitride (GaN) and its related group III alloys are the key material for various opto-electronic and electronic devices such as light emitting diodes (LEDs), laser diodes (LDs), microwave power transistors, and solar-blind photo detectors. Currently LEDs are widely used in cell phones, indicators, displays, and LDs are used in data storage discs. However, a majority of these devices are grown epitaxially on heterogeneous substrates, such as sapphire and silicon carbide, since GaN wafers are extremely expensive compared to these heteroepitaxial substrates. The heteroepitaxial growth of group III nitride causes highly defected or even cracked films, which hinders the realization of high-end optical and electronic devices, such as high-brightness LEDs for general lighting or high-power microwave transistors.

To solve fundamental problems caused by heteroepitaxy, it is useful to utilize single crystalline group III nitride wafers sliced from bulk group III nitride crystal ingots. For a majority of devices, single crystalline GaN wafers are favorable because it is relatively easy to control the conductivity of the wafer, and GaN wafer will provide smallest lattice/thermal mismatch with device layers. However, due to high melting point and high nitrogen vapor pressure at high temperature, it has been difficult to grow group III nitride crystal ingots. Growth methods using molten Ga, such as high-pressure high-temperature synthesis ([1] S. Porowski, MRS Internet Journal of Nitride Semiconductor, Res. 4S1, (1999) G1.3; [2] T. Inoue, Y. Seki, O. Oda, S. Kurai, Y. Yamada, and T. Taguchi, Phys. Stat. Sol. (b), 223 (2001) p. 15) and sodium flux ([3] M. Aoki, H. Yamane, M. Shimada, S. Sarayama, and F. J. DiSalvo, J. Cryst. Growth 242 (2002) p. 70; [4] T. Iwahashi, F. Kawamura, M. Morishita, Y. Kai, M. Yoshimura, Y. Mori, and T. Sasaki, J. Cryst Growth 253 (2003) p. 1), have been proposed to grow GaN crystals, nevertheless the crystal shape grown in molten Ga favors thin platelet formation because molten Ga has low solubility of nitrogen and a low diffusion coefficient of nitrogen.

An ammonothermal method, which is a solution growth method using high-pressure ammonia as a solvent, has demonstrated successful growth of bulk GaN ingots ([5] T. Hashimoto, F. Wu, J. S. Speck, S. Nakamura, Jpn. J. Appl. Phys. 46 (2007) L889). This newer technique called ammonothermal growth has a potential for growing large GaN crystal ingots, because high-pressure ammonia used as a fluid medium has high solubility of source materials, such as GaN polycrystals or metallic Ga, and has high transport speed of dissolved precursors. However, state-of-the-art ammonothermal method ([6] R. Dwiliński, R. Doradziński, J. Garczyński, L. Sierzputowski, Y. Kanbara, U.S. Pat. No. 6,656,615; [7] K. Fujito, T. Hashimoto, S. Nakamura, International Patent Application No. PCT/US2005/024239, WO07008198; [8] T. Hashimoto, M. Saito, S. Nakamura, International Patent Application No. PCT/US2007/008743, WO07117689; See also US20070234946, U.S. application Ser. No. 11/784,339 filed Apr. 6, 2007), can only produce brownish crystals. This coloration is mainly attributed to impurities. In particular, oxygen, carbon and alkali metal concentration of the sliced wafers from GaN ingots is extremely high. The brownish wafer shows large optical absorption, which deteriorates the efficiency of light emitting devices grown on such wafers.

Each of the references above is incorporated by reference in its entirety as if put forth in full herein, and particularly with respect to description of methods of making using ammonothermal methods and using these gallium nitride substrates.

SUMMARY OF THE INVENTION

The present invention provides a new production method for group III nitride wafers. In one embodiment of the invention, after group III nitride ingots are grown by the ammonothermal method, the ingots are sliced into pieces such as wafers having a thickness between about 0.1 mm and about 1 mm, for instance. Then, the pieces are annealed in a manner that improves transparency of the pieces and avoids dissociation and/or decomposition of the pieces. A surface portion of the pieces may then be removed if desired.

Resultant pieces such as wafers may differ from other ingot-derived or individually-grown pieces or wafers in their (1) transparency and (2) in their amount and/or distribution of impurities or their surface morphology resulting from having a surface layer removed, or both.

BRIEF DESCRIPTION OF THE DRAWINGS

Referring now to the drawings in which like reference numbers represent corresponding parts throughout:

FIG. 1 is a flow chart for the production of group III nitride wafers;

FIG. 2 is an example of the ammonothermal growth apparatus. 1 reaction vessel, 2 lid, 3 gasket, 4 heater for the dissolution region, 5 heater for the crystallization region, 6 convection-restricting device, 7 group III-containing nutrient, 8 nutrient basket, 9 group III nitride seed crystals;

FIG. 3 is the concentration of heavy metal impurities before and after the annealing in Example 1 measured by secondary ion mass spectroscopy (SIMS). The unit of the concentration is atoms/cm3.

FIG. 4 is the concentration of light metal impurities before and after the annealing in Example 1 measured by secondary ion mass spectroscopy (SIMS). The unit of the concentration is atoms/cm³.

DETAILED DESCRIPTION OF THE INVENTION

In the following description of the preferred embodiment, reference is made to the accompanying drawings which form a part hereof, and in which is shown by way of illustration a specific embodiment in which the invention may be practiced. It is to be understood that other embodiments may be utilized and structural changes may be made without departing from the scope of the present invention.

Technical Description of Aspects of the Invention

The present invention provides a method of producing group III (group 13) nitride wafers, primarily group III nitride single crystalline wafers that include at least one of the group III elements B, Al, Ga and In, such as GaN, AlN and InN. The process flow for one embodiment of the invention is indicated in FIG. 1. A group III nitride ingot is grown by the ammonothermal method, the ingot is cut into pieces, and the pieces are annealed preferably in a manner which limits or avoids dissociation and decomposition of piece surfaces. The pieces may be wafers as are typically used to form various semiconductor or optoelectronic devices, such as LEDs, laser diodes, solar cells, and photodetectors.

Ammonothermal Growth of Group III-Nitride Ingot

Ammonothermal ingot growth utilizes high-pressure NH₃ as a fluid medium, a nutrient containing at least one of the group III elements, and one or more seed crystals that are group III nitride single crystals. The high-pressure NH₃ provides high solubility of the nutrient and high transport speed of dissolved precursors. FIG. 2 shows an example of one ammonothermal reaction vessel in which the method may be carried out.

Methods of ammonothermal growth are discussed in WO08/51589 and in U.S. application Ser. No. 11/977,661, the contents of which are incorporated by reference in their entirety herein as if put forth in full below. The growth medium may therefore optionally contain a mineralizer. Basic mineralizers include Li, Na, K, LiNH₂, NaNH₂, and/or KNH₂. Acidic mineralizers include NH₄F, NH₄Cl, NH₄Br, and/or NH₄I.

Other ammonothermal growth methods may be used, such as those discussed in WO07/08198 and WO07/117689, which are incorporated by reference in their entirety herein as if put forth in full below.

The group III-nitride ingot (such as GaN) may be in the wurtzite crystal configuration or in the zincblende crystal configuration, for example.

Ingot Slicing

After a group III nitride ingot is grown, the ingot is sliced into wafers or crystalline pieces of other shape(s). An ingot may be sliced by any suitable equipment or method. A cutter such as a mechanical saw (e.g. a wire saw), a dicing saw, or a laser may be used. Wafers cut from the ingot may have a thickness between about 0.1 mm and about 1 mm, for instance. Wafers or other ingot pieces may be cut from an ingot along a Group III element face of the crystal (e.g. Ga face of the crystal, (0001) face, (000-1) face, {11-20} face, {10-10} face or other low index planes.

Annealing Wafer or Other Piece

Wafers or other ingot pieces are annealed to improve transparency and reduce impurities, preferably in a manner that limits or avoids substantial dissociation or decomposition of the pieces. Once pieces are cut from an ingot, those pieces may be individually or collectively annealed in an annealing reactor.

An annealing reactor may be configured to expose all surfaces of the piece (e.g. wafer) to an annealing gas in an annealing environment if desired. The annealing gas may be ammonia, hydrogen, a mixture of hydrogen and ammonia, or other gas that may create a reducing environment. While not being bound by theory, it is postulated that a reducing gas either maintains the pieces intact, without substantial degradation or decomposition or reacts with contaminants in the crystalline pieces, making the contaminants volatile and thereby removing the contaminants from the pieces, or both. The annealing gas may alternatively be an inert gas such as nitrogen, or the annealing gas may be a mixture of nitrogen, ammonia, and/or hydrogen and/or other gas that may create a reducing environment.

The annealing temperature may be selected to remove the amount of contaminant desired for removal. The temperature is sufficiently high to cause contaminants to migrate within the piece or pieces being annealed. For GaN, the temperature is often between about 500 and 1300° C. Typically, the temperature is at or above 500, 700, 800, 900, 1000, 1100, or 1200° C. in ambient gas comprising NH₃ and H₂. At about 1300° C., the pieces being annealed may decompose or etch somewhat. Consequently, it may be desirable to anneal at a temperature of no more than about 1300° C. in NH₃ and H₂ ambient. An annealing temperature of 1200° C. works well.

The pieces are annealed for a sufficient length of time to remove contaminants to a desired concentration in the pieces. Pieces may be annealed for at least about 15, 30, 45, or 60 minutes, for instance. If a lower temperature is used, often pieces may be annealed for a longer period of time to reduce contaminant concentration to the desired level. Although the annealing time depends on annealing temperature, the length of time that the pieces or ingot are annealed is sufficiently long to remove contaminants but not too long in order to avoid substantial degradation of crystal quality.

It has been observed that certain contaminants such as alkali metals concentrate at a Ga face of the crystal. Likewise, alkaline earth metals may concentrate at a Ga face. The annealing gas may be preferentially directed at the Ga face in order to reduce the concentration of these contaminants in the crystalline pieces or ingot. The length of time and annealing temperature may be selected based on the high concentration of these contaminants at a Ga face, and therefore the annealing conditions such as temperature and time may be different than for the case where these contaminants are dispersed throughout the crystalline pieces.

Annealing is typically carried out at atmospheric pressure (i.e. 1 bar). If the annealing temperature is close to the dissociation temperature, annealing can be carried out under pressure, for instance at or above 10 bar, 100 bar, or 1000 bar. On the other hand, if major contaminants are less volatile material, annealing can be carried out at subatmospheric or low pressure, for instance at or below 100 mbar, 10 mbar, 1 mbar, or less.

Ingot Annealing

A similar method can be utilized on the ingot itself. The ingot may be annealed in an annealing environment that limits or avoids substantial ingot dissociation or decomposition. The ingot may be annealed in addition to annealing pieces such as wafers cut from the ingot, or the ingot may be annealed instead of annealing its pieces.

Optional Surface Removal

Impurities may be further reduced by removing a surface layer of the wafers to which impurities have migrated. In one instance, at least a portion of a Group III element surface layer is removed (e.g. a Ga surface layer). Subsequent to ingot annealing, an outer surface or layer of the ingot may optionally be removed to reduce the concentration of the impurities in the ingot.

In some instances, any of the methods as discussed above reduce the concentration of heavy metals such as Ti, Cr, Fe, Ni, and Co (each metal alone or any combination of these heavy metals).

In some instances, any of the methods as discussed above reduce the concentration of alkali or alkaline earth metals such as Li, Na, Mg, and K (each metal alone or any combination of these metals). A portion of a surface layer may be removed that contains these metals, especially a Ga surface layer of the crystal of the ingot or wafer. The amount of surface of wafers or ingot that may be removed can vary depending upon how much impurity can be tolerated in the wafer or ingot during use.

Further Considerations

The amount of impurity may be reduced by any method above to no more than about 60%, 50%, 40%, 30%, 20%, 15%, 10%, or 5% of the concentration of that impurity at a face (e.g. Ga or other group III element or nitride face) prior to annealing. Annealing may reduce the level of the contaminant to below a detectable level. See in particular the tables in FIGS. 3 and 4, which indicate how much the concentration was reduced for various contaminants at the Group III element face and the nitride face. The concentration of contaminants was measured with secondary ion mass spectroscopy (SIMS).

The contaminant removed may be a metal. Alkali and alkaline earth metals may be removed in certain embodiments. Likewise, heavy metals selected from transition metals (e.g. Ti, Cr, Fe, Ni, and Co), metalloids such as Ge or heavier, rare earth metals, and other metals having similar atomic weight may be removed. The concentration of heavy metal impurities such as Ti, Cr, Fe, Ni or Co may be less than about 1×10¹⁷ cm⁻³ after an ingot or pieces are treated according to a method herein. The concentration of light metals (metals such as Li, Na, K, and Mg) may likewise be less than about 1×10¹⁷ cm⁻³ after an ingot or pieces are treated according to a method herein.

The annealing above differs from annealing after e.g. implanting a crystalline material with a dopant. Typically a substrate is annealed after implanting dopant atoms in order to diffuse the atoms to a certain depth and therefore decrease the concentration of the dopant in the substrate at the point of implantation. In the method of the invention, impurities may be concentrated locally (such as at a group III element face of the crystalline structure) rather than diffused, and/or impurities may be removed from the substrate by annealing it.

The annealed pieces or ingot may be used to form various electronic or optoelectronic devices. Electronic and optoelectronic devices include those disclosed in U.S. application Ser. No. 11/765,629, filed Jun. 20, 2007 and entitled “Opto-Electronic and Electronic Devices Using N-Face or M-Plane GaN Substrate Prepared With Ammonothermal Growth”, the contents of which are incorporated by reference herein in their entirety as if put forth in full below.

The following examples describe a detailed procedure within the scope of the current invention to help illustrate the invention further.

Example 1

In this example, a reaction vessel having an inner diameter of 1 inch was used for the ammonothermal growth. All necessary sources and internal components including 10 g of polycrystalline GaN nutrient held in Ni mesh basket, 0.3 mm-thick single crystalline GaN seeds, and three baffles, which acts as a flow restriction device were loaded into a glove box together with the reaction vessel. The glove box is filled with nitrogen and the oxygen and moisture concentration is maintained to be less than 1 ppm. Since the mineralizers are reactive with oxygen and moisture, the mineralizers are stored in the glove box all the time. 4 g of as-received NaNH₂ was used as a mineralizer. After loading mineralizer into the reaction vessel, three baffles together with seeds and nutrient are loaded. After closing the lid of the reaction vessel, it was taken out of the glove box. Then, the reaction vessel is connected to a gas/vacuum system, which can pump down the vessel as well as can supply NH₃ to the vessel. First, the reaction vessel was evacuated with a turbo molecular pump to achieve pressure less than 1×10⁻⁵ mbar. The actual pressure in this example was 1.2×10⁻⁶ mbar. In this way, residual oxygen and moisture on the inner wall of the reaction vessel are partially removed. After this, the reaction vessel was chilled with liquid nitrogen and NH₃ was condensed in the reaction vessel. About 40 g of NH₃ was charged in the reaction vessel. After closing the high-pressure valve of the reaction vessel, it was transferred to a two zone furnace. The reaction vessel was heated to 575° C. of the crystallization zone and 510° C. for the dissolution zone. After 7 days, ammonia was released and the reaction vessel was opened. The total thickness of the grown GaN ingot was 0.99 mm.

Since the thickness of the ingot was less than 1 mm, the ingot shape was already wafer-like without slicing. The wafer-like ingot had Ga-polar (0001) surface and N-polar (000-1) surface as basal planes. The wafer-shaped ingot was then loaded into an annealing reactor. The wafer-shaped ingot stood on its edge so that the both sides of the basal planes were exposed to the gas stream. After evacuating the air in the reactor, forming gas (4% H₂/96% N₂) was introduced to the reactor. Then, the reactor was heated. At 485° C., ammonia was introduced to the reactor to suppress dissociation or decomposition. The flow rate of ammonia and the forming gas was 1 slm and 1.1 slm, respectively. The wafer-shaped ingot was annealed at 1100° C. for about 1 hour. Then, the reactor was cooled. At about 400° C., ammonia was shut off.

The coloration in a wafer-like ingot prepared as described above was observably reduced when its coloration was compared to the coloration of a wafer-like ingot that was not annealed. This reduction in coloration in the annealed ingot indicates the reduction of impurities. The impurity quantification by secondary ion mass spectroscopy (SIMS) confirmed reduction of heavy metals such as Ti, Cr, Fe, Ni, and Co as shown in FIG. 3. On the other hand, light metals such as alkali metals and alkali earth metals moved toward Ga-polar surface. As shown in FIG. 4, the concentration of Li, Na, Mg, and K increased after annealing on the Ga-polar side whereas it decreased on the N-polar side. This suggests that alkali metals and alkali earth metals are positively charged and they are attracted by the surface charge on the Ga-polar surface, resulting in accumulation of these impurities on the top Ga-polar surface. Therefore, we can efficiently remove alkali metals and alkali earth metals from the wafer with annealing followed by removing a portion of the Ga-polar surface by e.g. grinding, lapping, polishing, or etching the Ga-polar surface.

Example 2

In this example a GaN ingot was formed by the same method as described in Example 1. The GaN ingot was sliced into 0.4 mm-thick wafers with a wire saw. Then 6 wafers were annealed at different temperatures (500, 700, 900, 1100, 1200, and 1300° C. in NH₃ ambient for 1 hour) by the following process.

A wafer was placed into a reactor. After evacuating air in the reactor, a forming gas (4% H₂/96% N₂) was introduced into the reactor, and subsequently the reactor was heated. At 485° C., ammonia was introduced to the reactor to suppress dissociation or decomposition of the GaN. The flow rate of ammonia and the forming gas was 1 slm and 1.1 slm, respectively. During annealing both the Ga-face and the N-face of each wafer was exposed to the ambient gas. When the GaN wafer was annealed at 1300° C., the surface of the wafer was etched away. Therefore, if ammonia is used to suppress dissociation or decomposition, the temperature is typically less than 1300° C. to avoid surface etching during annealing.

Properties of wafers annealed by the method above were compared to an unannealed wafer. Each wafer has three regions: a Ga-face region; a seed region; and a N-face region from the left in each wafer. The unannealed wafer had a dark N-face region and a slightly tinted Ga-face region together with a clear seed region. The coloration on the Ga-face was reduced with annealing even at 500° C. Slight reduction of coloration was observed for wafers annealed at 500, 700, 900, and 1100° C. Annealing at 1200° C. made a drastic change: the N-face region showed much brighter color although the seed region and the Ga-face region showed slight coloration. Therefore, annealing at 1200° C. is effective for N-face region.

The following theory is of course not limiting on the scope of the invention. The difference in the coloration in the seed region and the Ga-face region implies that coloration is not only governed by an impurity, but also by native defects such as point defects. From the color change in the N-face region, it is believed that some impurities diffused out from the N-face region, thus the N-face region acted as an impurity source. The seed region, which was closer to the N-face region must have higher impurity concentration than Ga-face region which is farther from the N-face region. Therefore, if coloration is only due to impurity concentration, one might expect the seed region to be darker than the Ga-face region. However, the seed region was brighter than the Ga-face region. This implies that the Ga-face region originally had higher defects which, when combined with an impurity, will act as a color center. Therefore, it appears to be desirable to reduce native defects such as point defects in the ammonothermally grown group III-nitride crystals.

From this example, we found that annealing in ammonia is preferably performed at a temperature less than 1300° C. when surface etching of GaN is not desired, preferably between 500 and 1300° C., or more preferably between 1100 and 1300° C. The pressure may be about 1 bar, or the pressure may be sub-atmospheric or above atmospheric pressure as discussed above.

Advantages and Improvements

The present invention provides a new production method for group III nitride wafers with improved transparency and purity. Annealing the wafers after slicing is an effective way to reduce impurities in the crystal since the necessary time for the impurities to diffuse out of the crystal can be much smaller than the situation of annealing the ingot before slicing. The purified wafer showed improved transparency which improves efficiencies of optical devices fabricated on the wafers.

CONCLUSION

This concludes the description of the preferred embodiment of the invention. The following describes some alternative embodiments for accomplishing the present invention.

Although the preferred embodiment describes the growth of GaN as an example, other group III nitride crystals may be used in the present invention. The group III nitride materials may include at least one of the group III elements B, Al, Ga, and In.

Although the preferred embodiment describes the annealing of ingots or wafers in ammonia ambient, other method to avoid dissociation or decomposition can be used. For example, covering the wafer surface with a silicon oxide layer, a silicon nitride layer, a metal layer or other protective layer is expected to be effective way to avoid dissociation and decomposition of the wafer. One or more of these layers may be deposited on a wafer using e.g. chemical vapor deposition or sputtering. If desired, the protective layer or layers may be removed using conventional etching techniques immediately before using a wafer to form a device.

Although the preferred embodiment describes the annealing at 1100-1200° C. for 1 hour or other time sufficient to improve wafer clarity, other temperatures and/or times can be utilized so long as the same or similar benefit can be obtained.

In the preferred embodiment specific growth apparatuses and annealing apparatus are presented. However, other constructions or designs that fulfill the conditions described herein will have the same benefit as these examples.

The present invention does not have any limitations on the size of the wafer, so long as the same benefits can be obtained.

The foregoing description of the preferred embodiment of the invention has been presented for the purposes of illustration and description. It is not intended to be exhaustive or to limit the invention to the precise form disclosed. Many modifications and variations are possible in light of the above teaching. It is intended that the scope of the invention be limited not by this detailed description, but rather by the claims appended hereto. 

What is claimed is:
 1. A method of removing a contaminant from a group III nitride single-crystalline wafer comprising: a. annealing the wafer, which has a N-face and a group III-face, in an ambient containing ammonia vapor for a time at a temperature and pressure that concentrate a contaminant toward the group III-polar face, thereby forming a region of concentrated contaminant in the group III-polar face; and b. removing a sufficient amount of the crystalline wafer at the group III-polar face to reduce a thickness of the crystalline wafer and to remove at least a portion of the region of concentrated contaminant; c. wherein the contaminant is selected from an alkali metal and an alkaline earth metal.
 2. The method of claim 1, wherein the contaminant comprises at least one of sodium and lithium.
 3. The method of claim 1, wherein the contaminant comprises potassium.
 4. The method of claim 1, wherein the contaminant comprises magnesium.
 5. The method of claim 1, wherein sufficient ammonia vapor is present to suppress decomposition of the wafer.
 6. The method of claim 1, wherein the contaminant is positively charged.
 7. The method of claim 1, wherein the annealing conditions also reduce a concentration of a heavy metal at both the N face and the group III face.
 8. The method of claim 7, wherein the heavy metal is selected from the group consisting of Ti, Cr, Fe, Ni, and Co.
 9. The method of claim 1, wherein the annealing is performed at a temperature greater than or equal to 1100° C.
 10. The method of claim 1, wherein the annealing is performed at a temperature greater than or equal to 1200° C.
 11. The method of claim 1, wherein the annealing is performed at a sufficiently high temperature to reduce a number of point defects in the wafer.
 12. The method of claim 1, wherein the group III nitride single-crystalline wafer comprises gallium.
 13. The method of claim 1, wherein the group III nitride single-crystalline wafer was formed using an ammonothermal process.
 14. A single-crystalline wafer formed by an ammonothermal process having, at an N-face of the wafer, a concentration of lithium about equal to or less than 4×10¹³ or a concentration of potassium about equal to or less than 3×10¹⁴ cm⁻³.
 15. A single-crystalline wafer formed by an ammonothermal processing having, at an N-face of the wafer, a concentration of chromium about equal to or less than 6×10¹⁴ cm⁻³ or a concentration of nickel of about equal to or less than 1×10¹⁶ cm⁻³. 